Discrete-time Implementation Research Articles

Adaptive Control for Improved Transparency in Haptic Simulations.

Two adaptive nonlinear controllers are proposed for the coupling of haptic devices with impedance-type and admittance-type virtual environments, respectively. Rigid contacts in admittance-type environments are modeled either as a stiff spring or a constraint on the haptic device motion. Both controllers employ user position and force measurements to replace the natural dynamics of the haptic interface with that of an adjustable mass-damper tool. The transparency and stability of the resulting systems are investigated using a Lyapunov analysis and by taking into account uncertain nonlinear dynamics for the haptic device, and uncertain mass-spring-damper type dynamics for the user and virtual environment. It is shown analytically that low-pass filtering of selected terms in the control signal can significantly reduce a stability related lower bound on the achievable synthesized mass of the haptic interface in a discrete-time implementation of the controllers. An optimization problem is formulated and solved to balance impedance reduction against noise amplification in choosing the filter gain and bandwidth. The proposed controllers as well as a conventional penalty-based method are compared in a set of experiments. The results indicate that the controller with an admittance-type constraint-based rigid environment has far superior performance in terms of the range of impedances that it can stably display to the user.

Closed-Loop Control of an Underactuated Sheet Registration Device Using Feedback Linearization and Gain Scheduling

Over the past few decades, the two-wheeled driven cart, also known as the unicycle wheeled mobile robot or wheeled mobile robot with independently driven wheels, has been a favorite case study in the literature on nonholonomic control. In this paper, we show how input-output linearization of a cart can be leveraged for a novel and practical application, closed-loop control of a differential-drive sheet registration device. The current state of the art for control for such a device, typically found in xerographic engines like printers and copiers, is open-loop motion planning. We present a closed-loop method that achieves full-state trajectory tracking via input-output linearization and asymptotically stable internal dynamics. To achieve rapid convergence while satisfying acceleration constraints, we apply elementary gain scheduling to the output tracking controller of the linearized input-output system. Experimental results are presented to demonstrate the effectiveness of the discrete-time implementation of our control strategy, which is based on a kinematic model with acceleration as the control input.

Precision control of third-order profile planning for high accuracy point-to-point motion system

A third-order profile planning method and precision control strategies for point-to-point motion are studied. Several crite- rions are presented relying on all possible instances for third-order profile planning. Based on these criteria and dynamic constraints, fast and accurate algorithm of profile planning with time-optimality by preprocessing the entire profile as a whole is described. Ac- curacy losses in discrete time implementation are considered. As a result, an internal integer data integration strategy and a compen- sation approach based on correcting factor are investigated. Finally, experiment results demonstrate the effectiveness and reliability of the proposed methods. The presented method is successfully applied in semiconductor manufacturing equipments.

Nonstationary Motor Fault Detection Using Recent Quadratic Time–Frequency Representations

As the use of electric motors increases in the aerospace and transportation industries where operating conditions continuously change with time, fault detection in electric motors has been gaining importance. Motor diagnostics in a nonstationary environment is difficult and often needs sophisticated signal processing techniques. In recent times, a plethora of new time-frequency distributions has appeared, which are inherently suited to the analysis of nonstationary signals while offering superior frequency resolution characteristics. The Zhao-Atlas-Marks distribution is one such distribution. This paper proposes the use of these new time-frequency distributions to enhance nonstationary fault diagnostics in electric motors. One common myth has been that the quadratic time-frequency distributions are not suitable for commercial implementation. This paper also addresses this issue in detail. Optimal discrete-time implementations of some of these quadratic time-frequency distributions are explained. These time-frequency representations have been implemented on a digital signal processing platform to demonstrate that the proposed methods can be implemented commercially.

On Feedback Linearization for Robust Tracking Control of Flexible Joint Robots

Feedback linearization is one of the major academic approaches for controlling flexible joint robots. This contribution investigates the discrete-time implementation of the feedback linearization approach for a realistic three-axis robot model. A simulation study of high speed tracking with model uncertainty is performed. It is assumed that full state measurements of the linearizing states are available. The feedback linearization approach is compared to a feedforward approach.

High Performance Repetitive Control of an Active Filter under Varying Network Frequency

Shunt active power filters are power electronics devices that are connected in parallel with nonlinear and reactive loads to compensate these characteristics in order to assure the quality of service of the electrical distribution network. This work proposes and designs a controller, based on combined feedforward and feedback actions, the last using repetitive control, to obtain a good closed-loop performance (power factor close to 1 and, load current harmonics and reactive power compensation) in spite of the possible frequency variations that may occur in the electrical network. It is known that these variations clearly affect the performance of the usual discrete-time implementations of the repetitive based controllers. This work analyzes the effect of these variations and describes the architecture of the controller, its design, and the mechanism to compensate the network frequency variations. Some experimental results that show the good performance of the closed-loop system are also included.

A Sampled-Data Scheme for Disturbance Rejection of Nonlinear Systems in Output Feedback Form

This paper presents a sampled-data control scheme for disturbance rejection of nonlinear systems in output feedback form. The continuous-time controller is designed first using a filtered transformation and the internal model technique. Obtained on an emulation-based approach, the proposed sampled-data control uses the sampled output and a discrete-time implementation of the filter and the internal model is involved. The proposed control is shown to render the overall system stable in a spirit of fast sampling. Specifically, the ultimate bound of the output is allowed to be arbitrarily small by choosing appropriate gain parameters.

Discrete vs. continuous time implementation of a ring car following model in which overtaking is allowed

Car following models seek to describe the interactions between individual vehicles as they move along a stretch of road where the behaviour of each vehicle is dependent on the motion of the vehicle directly in front and overtaking is typically not permitted. In this work we study a modified version of the traditional car following model in which the vehicles are travelling on a closed loop and the ‘no overtaking’ restriction has been removed. The resulting model is described firstly in terms of a set of coupled continuous time delay differential equations and then in terms of their discrete time equivalents and both forms of the model are then solved numerically to analyse their post transient behaviour under a periodic perturbation. For certain parameter choices both the continuous and discrete forms of the model can exhibit chaotic behaviour but a comparison of the behaviour of the two models over a wide range of parameter values shows that the discretization can dramatically affect the type of post transient behaviour exhibited. This becomes increasingly evident as the time step used in the discrete time model is increased.

On observer design for nonlinear systems

The main weakness of all control methodologies is the dependency of feedbacks to full state measurements. In practical situations, measuring the states of a given system may fail because sometimes the measurements are impossible and sometimes, possible, but too expensive. Observer design for highly nonlinear dynamics is an important issue, particularly when the locally observable dynamics are not linearly observable. In such circumstances the ability to reduce the system to observable or observer form is key to observer design. This paper provides two observers for nonlinear systems given in Brunovski form. The first observer is a high-gain observer with a classical output injection form, while the second is a high-gain observer with a q-integral path. Finally, the discrete-time implementation of the high-gain observer is discussed in linear matrix inequality framework. A motivating example is shown to highlight the efficacy of the developed observers.

BER performance analysis of the discrete time and the continuous time Rake receivers for the UMTS downlink

The paper gives the bit error rate (BER) expressions of the continuous time and discrete time Rake receivers (CTR and DTR) for the UMTS downlink. The former receiver is the most used and consists in combining the output of correlators locked on the most significant paths. Since the conventional synchronization module of the CTR is hot able to distinguish close paths, a discrete time implementation of the Rake receiver which circumvents the problem of path delay estimation was proposed in previous papers. The DTR consists in a matched filter to the discrete time equivalent model of the global channel resulting from the convolution of the impulse response of the transmitter shaping filter and the multipath channel. Using the assumption of Gaussian noise on the receiver output, we derive the BER expressions of both the CTR and DTR. The obtained expressions are valid for any multipath channel and take simultaneously into account path gain estimation noise, the intersymbol interference and the multiuser interference which is a realistic scenario for the UMTS downlink. Based on this theoretical study, a power control policy is also formulated.

Extending the universality of the Heath–Jarrow–Morton model

Heath, Jarrow, and Morton (HJM) developed an important model of the evolution of interest rates. A key assumption of the model is that interest rate changes are normally distributed in continuous time. Implementing the HJM-method of evolution of interest rates in discrete time for more complex volatility functions remains a significant challenge. In this article, we present a relatively simple and flexible method of implementation, that extends the usefulness of the HJM model. The derivation assumes that the distribution of interest rates is stable, but not necessarily identical, for each discrete time period. This allows us to identify the drift-adjustment terms necessary to build interest rate lattices and trees and Monte Carlo simulations that satisfy exactly the no-arbitrage and volatility conditions, even complex ones, of the model. The much more difficult discrete-time implementation methods suggested in the literature (Heath, Jarrow, and Morton (1991) [Heath, D., Jarrow, R. & Morton, A. (1991). Contingent claim valuation with a random evolution of interest rates. Review of Futures Markets, 54–76.] and Jarrow (1996) [Jarrow, R. (1996). Modeling fixed income securities and interest rate options. New York, NY: McGraw-Hill Companies Inc.]) do not accomplish that. We illustrate our analytical implementation with three examples of volatility functions and demonstrate its superiority to other methods of implementation.

Performance Analysis of a High-Bandwidth Torque Disturbance Compensator

Recent availability of encoder with millions of counts per revolution makes it possible to enlarge the bandwidth of the torque disturbance observer (TDO) equipping a servo drive. As a consequence, the TDO dynamics are no more decoupled from those of current and the behavior of the torque disturbance compensator (TDC) is influenced by the current dynamics as well as by the discrete-time implementation of TDO. The purpose of this paper is to analyze the TDC performance under the above-mentioned circumstances. The main outcome is the underdamped or even unstable behavior of TDC. Another outcome is the limited range of values allowable for the parameter mismatch to preserve stability. The conditions on the TDO bandwidth and the parameter mismatch for TDC to be stable and to be damped are provided. Experimental tests are given, which substantiate the theoretical findings.

Discrete-time analysis of HHC schemes for helicopter vibration attenuation

Higher Harmonic Control (HHC) algorithms for helicopter vibration reduction are analysed by taking into account the issues related with their discrete-time implementation. In particular, the periodicity of helicopter dynamics and the presence of two different sampling rates in the control loop are dealt with using a lifted reformulation of the closed loop system, which turns out to be time-invariant. Finally, a numerical investigation of the stability characteristics of HHC control loops is carried out and discussed in order to assess the role of digital implementation in determining the stability and performance of the vibration control system.

On the Use of Controller Parametrization in the Optimal Design of Dynamically Operable Plants

This paper explores some issues pertaining to the use of Q-parametrization in the optimal design of dynamically operable plants. An optimization based plant design formulation in which a discrete-time implementation of the controller parametrization is embedded, is described. Its application is demonstrated through a reactor case study in which the resulting design is compared against that obtained using PI control. Differences in results obtained are discussed and related to the design problem formulation. The impact of other assumptions, such as the disturbance dynamics, is also discussed.

Robust nonlinear control of single limb movement

The aim of this work was to design a robust nonlinear controller for the knee-joint angle by means of Functional Electrical Stimulation (FES). It is well known that a good mechanical model of the body segments can be obtained by first principles and simple pendulum tests, while it is hard to obtain a good model of the electrically elicited muscle contractions for control purposes due to time-variant and nonlinear properties of the muscles combined with limited measurements. For this reason the muscle activation dynamics are only modeled as a first order linear system. To describe how the muscle contraction depends on joint angle and velocity a simplified linear static function was introduced. Based on this model a nonlinear control design approach is performed applying the back-stepping methodology. This design approach is highly attractive as it can easily be extended to multivariable systems with many body segments and muscle groups, and it allows nonlinear muscle models to be incorporated into the control design. A simulation study of the controller is carried out using a physiologically based model of the neuro-musculoskeletal system as a substitution of the real plant. Robustness and performance of the designed controller, also with respect to the discrete-time implementation and an unmodeled time delay are discussed.

Discrete time adaptive reaching law speed control of electrical drives

This paper describes an adaptive control scheme for servomotor speed control systems under inertial and frictional variations. The control is based on reaching law control (RLC), which is an approach to sliding mode control (SMC) design. The adaptations of the control parameters are performed using the gradient descent method. Discrete time implementation of the SMC strategy is considered in the paper, since it is more appropriate for practical applications. It is shown that the robustness of the SMC method is constrained by sampling time. Also shown is the deterioration of the speed responses under the plant parameter variations due to finite sampling time. Thus, an adaptation mechanism for the control parameters is introduced in order to provide a robust control performance under the plant parameter variations. Practical implementation of the proposed control scheme is also discussed in the paper.

Control and filter design of three-phase inverters for high power quality grid connection

The trend toward using inverters in distributed generation systems and micro-grids has raised the importance of achieving low-distortion, high-quality power export from inverters. Both switching frequency effects and pre-existing grid voltage distortion can contribute to poor power quality. A well designed filter can attenuate switching frequency components but has an impact on the control bandwidth and the impedance presented to grid distortion. This paper describes a filter designed to incorporate an isolating transformer and the design of a complementary controller that rejects grid disturbance, maintains good waveform quality and achieves real and reactive power control. A realistic discrete time implementation is discussed and validated with experimental results.

The Use of Real-World Computer Models for Computer-Aided Design of Tracking Control Schemes for Induction Motors

The design of tracking controllers for induction motors is usually developed by neglecting the presence of power-supply devices, such as inverters, and measurement apparatuses, e.g., encoders. However, these components represent unmodeled dynamics that are present during the real operating conditions of the induction motor. Since the development of a numerical simulation study represents a low-cost, safe, and fast test to validate the design of tracking control schemes, the need arises to build a computer model of the overall system (i.e., motor, power supply, measurement devices, and tracking controller) as realistic as possible. In this context, the paper describes a computer model for simulation of an induction motor under a tracking control scheme including many real-world effects; namely, encoder's quantization, current sensors' noise, stator current dynamics, presence of a current-controlled voltage-source inverter within a stator current regulator loop, flux observer dynamics, saturation of the control signal, and discrete-time implementation of the control algorithm. The developed computer model is finally used in a case study and the simulation results obtained for an induction motor driving a single-link robotic arm under an H8 tracking control scheme are reported.

Efficient arbitrary sampling rate conversion with recursive calculation of coefficients

In this paper, we present a novel algorithm for sampling rate conversion by an arbitrary factor. Theoretically, sampling rate conversion of a discrete-time (DT) sequence can be performed by converting the sequence to a series of continuous-time (CT) impulses. This series of impulses is filtered with a CT lowpass filter, and the output is then sampled at the desired rate. If the CT filter is chosen to have a rational transfer function, then this system can be simulated using a DT algorithm for which both computation and memory requirements are low. The DT implementation is comprised of a parallel structure, where each branch consists of a time-varying filter with one or two taps, followed by a fixed recursive filter operating at the output sampling rate. The coefficients of the time-varying filters are calculated recursively. This eliminates the need to store a large table of coefficients, as is commonly done.

Discrete type dynamic synapses neural network: Speech recognition application

A discrete type of the Dynamic Synapses Neural Network (DSNN) has been developed and applied to speech recognition. In order to speed up the training time of the network, a new discrete time implementation of the original DSNN [J.-S. Liaw and T. W. Berger, 1996] has been introduced based on the impulse invariant transformation. The new architecture of the network was trained with the Genetic Algorithms [H. H. Namarvar et al., 2001] and tested against the continues-type DSNN. The overall speed of the new algorithm with discrete-time difference equation set is about 13 times faster than the same algorithm with the continuous differential equation set. This significant reduction of processing time not only decreases the training time but also makes the system better suited for real-time speech recognition tasks. [Work supported by DARPA.]